Bio-fuel multi-stage activity modelling to determine efficient public policy in uncertain agricultural markets

Support policy to biomass-origin liquid fuels incorporated in gasoline and diesel has been implemented during the last decade in France through tax exemptions to bio-fuels. Tax exemption levels as well as production agreements determining beneficial quantities are allocated by the government depending on an earmarked budget revised every year by the parliament. A partial equilibrium model with a detailed agricultural sector component that is formed by a large number of representative farms producing energy crops (wheat, sugar-beet and rapeseed) jointly with food crops, is used to estimate costs and surpluses generated by the bio-fuel production activity at the national level. The aggregate supply of energy crops is estimated using a staircase model of elementary farm sub-models specialising in arable cropping. The government acts as a leader since bio-fuel chains depend on subsidies. The model provides the industry reaction to policy schemes, taking into account the energy crop producers’ supply response curve. A multi-criteria optimisation module can assist the policy maker to select policies that serve budgetary, environmental and social concerns by approaching decision-maker’s objectives at the closest feasible compromise levels. In order to enhance the predictive ability of such a model, interval linear programming (ILP) is used to consider uncertainty related to yields and prices and its impact to the farmer behaviour. Besides the expected gross margin maximisation rationale, the distance from optimality once uncertainty resolves (maximum regret) is a useful criterion that farmers apply in many cases. A hybrid mathematical programming model is then set up articulating custom utility functions for each individual farmer according to observed behaviour and the specific properties of each farm. Energy crop supply curves generated by the hybrid model proved to be slightly deplaced to the right (less costly energy crops) but still upward sloped.